1.İngiltere'ye hiÃƒÂ§ gittin mi?
can be
a)Have you ever been to England?
b)Did you ever be to England?
hiÃƒÂ§ is ever.
So, I think that the correct answer should be a.
Because we learned that 'ever' is used with Have/Has.
But grammatical translation should be b.
What is is the difference between a and b?
As a Turk, it is not very clear for me...

2.Anahtarlarımı kaybetmişim.
I think we cannot translate this to English. I mean with the same grammar.
I wasn't aware that I had lost my keys sometime(unknown) in past. You say that, when(NOW) you needed to use your keys but discovered that they are not in your pocket.(NOW)
a)I lost my keys.
b)I have lost my keys.
Which one is close to my explanation?

Anahtarlarımı kaybettim.
I know that I have lost my keys. I can also tell the time when I lost them. Or you have already discovered that you had lost your keys before arriving in front of the door. So I can't open the door. You don't try to look for your keys, since you know you have lost them.
a)I have lost my keys.
b)I lost my keys.
Which one is close to my explanation?

3.a)Son zamanlarda ne yapıyorsun? -> You are asking if the action still continues. Action started in past but still continuing. Here, son zamanlarda(lately) gives enough information for the time(started in past) and -yor marks the continuous progress.
a)What have you been doing lately?
b)What are you doing lately?
b is grammatical translation. a is the correct one.
That you started an action which still continues.

b)Son zamanlarda ne yapıyordun? -> You are asking with the thought of the action might be ended. Action started in past and ended in past. Relatively close to NOW. Because you said son zamanlarda. -yordu marks that the action which was continuous in the past has ended.
a)What have you been doing lately?
b)What were you doing lately?
Which one do you choose?

4.EylÃƒÂ¼lden beri burada ÃƒÂ§alışıyorum. --> Action started in past is still in progress. Here, beri also marks it is a continuing progress.
a)I have been working here since September.
b)I am working here since September.
b is grammatical translation, a is the meaning translation.
I started working in September and I am still working here.

EylÃƒÂ¼lden bu yana burada ÃƒÂ§alışıyordum. Action started in past has come to end lately. Since we said 'bu yana' (--> until now).
***We need to change 'beri' to 'bu yana' in the above sentence. In talking language you may use beri but it should be bu yana in grammar. Since beri marks a continuous progress. And 'bu yana' is the same meaning but can be used with an action which is ended or still continuing.
***Actually I am not sure about this(beri/bu yana). It is better to ask someone who has more knowledge than me. But I feel like above.
a)I have been working here since September.
b)I was working here since September.
Which one describes better? a or b?

Finally; -mış/-miş:
1.Used in almost all stories. Describing an action that you weren't there when it happened, so you just heard of it from someone else.
**Ali okula gitmiş. -->
(I asked her mother,father etc) They said that Ali had gone to school.
2.It may also describe that you are not sure of it. or amazed/surprised/shocked of hearing it. Mostly depends on your intonation. You are not sure because you weren't there.
**Ali Ayşe'yi ÃƒÂ¶ldÃƒÂ¼rmÃƒÂ¼ş.
You are not sure if Ali is the murderer. You just heard that he killed her.
Or you are shocked to hear that Ali had killed Ayşe. Latter depends on your intonation.

3.Also used to tell that 'someone' was not aware of something. And you became aware recently.
**Anahtarlarımı kaybetmişim.

**Araba kazası yapmışsın. It looks like you had an car accident,(you just saw his car and have been aware of that there had been a car accident.(NOW))
That can also mean, you heard that he had an car accident, without seeing his car. Say; you are talking in a place where you can't/couldn't see the car.

**Gece kar yağmış. (I saw that in the morning)

It will be nice to see your answers for 1, 2, 3 and 4.
So I can refresh my memory for Past and Perfect.

2.Anahtarlarımı kaybetmişim.
I think we cannot translate this to English. I mean with the same grammar.
I wasn't aware that I had lost my keys sometime(unknown) in past. You say that, when(NOW) you needed to use your keys but discovered that they are not in your pocket.(NOW)
a)I lost my keys.
b)I have lost my keys.
Which one is close to my explanation?

I think a good translation would be: "I seem to have lost my keys.."You suddenly realise that you might have lost them, but you didn't see it happening of course. So because you assume you have lost them, you use the -miş tense..